PHYSICS1. The diagram shows two antiparallel current that

are equal to magnitude AB is a line perpendicularto both the currents and O is its centre. Considernow the following statements

O

A

B(i) The resultant magnetic field at O is non-

zero(ii) The magnitude of magnetic field among AB

is constant(iii) The direction of the magnetic field among

is same every where on AB. Which of thefollowing is correct?

(a) (i), (ii) and (iii) (b) (i) and (ii)(c) (i), and (iii) (d) (ii) and (iii)

2. The ionisation potential of hydrogen atom is 13.6V. The energy needed to ionise a hydrogen atomwhich is in its second excited state is about(a) 3.4 eV (b) 1.5 eV(c) 10.2 eV (d) 13.6 eV

3. Consider the following processes(i) Electrical oscillation(ii) Rapid deceleration of fast electrons(iii) Atomic transitionWhich of these are likely to produce visible light?(a) (iii) only (b) (ii) and (iii)(c) (i) and (iii) (d) (i), (ii) and (iii)

4. An inductor and a resistor in series areconnected to an AC supply of variablefrequency. As the frequency of source isincreased, the phase angle between current andpotential difference across L will

General InstructionsPhysics : Question no. 1 to 40 (total 40 questions)Chemistry : Question no. 41 to 80 (total 40 questions)Mathematics : Question no. 81 to 125 (total 45 questions)English Proficiency : Question no. 126 to 140 (total 15 questions)Logical Reasoning : Question no. 141 to 150 (total 10 questions)Marking Scheme : For each correct answer 3 marks will be awarded and 1 mark will be deducted

for indicating incorrect response of each questions.

Time allowed: 3 hours Maximum marks: 450

MOCK TEST - 1

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2(a) go on increasing(b) go on decreasing(c) first increase then decrease(d) first decrease then increase

5. A thin oil layer floats on water. A ray of lightmaking an angle of incidence 40 shines an oillayer. The angle of refraction of light ray in wateris (oil = 1.45, water = 1.33)(a) 28.9 (b) 26.8(c) 44.5 (d) 36.1[sin 40 = 0.6428, sin 44.5 = 0.7007]

6. An achromatic prism is made by combination oftwo prism P1 (F = 1.523, C = 1.515) and P2 (F= 1.616, C = 1.650). If the angle of prism P1 is 10then the angle of prism P2 will be(a) 2.4 (b) 10.6(c) 7.8 (d) 5

7. A drop of water is placed on a glass plate. Adouble convex lens having radius of curvatureof each surface 20 cm is placed on it. The focal

length of water lens 3for water4

= , will be

(a) 0.20 m (b) 0.60 m(c) 0.30 (d) 0.40 m

8. A force of 106 N/m2 is required for bearing amaterial. If the density of the material is 3 103kg/m3, then what should be the length of thewire made of material so, that it breaks by itsown weight ?(a) 17 m (b) 34 m(c) 26 m (d) 23 m

9. The surface tension of water is 7 102 N/m.The weight of water supported by surfacetension in a capillary tube of 0.1 mm radius, will

be(a) 44 106 N (b) 22 106 N(c) 33 106 N (d) none of these

10. A rain drop of radius 0.3 mm has a terminalvelocity of 1 m/s in air. The viscosity of air is18 105 poise. The viscous force on the drop is(a) 16.695 107 N (b) 1.695 108 N(c) 1.017 1011 N (d) 101.73 109 N

11. When temperature is increased from 0C to273C, in what ratio the average kinetic energyof molecules change ?(a) 1 (b) 3(c) 4 (d) 2

12. The root means square speed of hydrogenmolecules of an ideal hydrogen gas kept in a gaschamber at 0C is 3180 m/s. The pressure ofhydrogen gas will be (Density of hydrogen gas= 8.99 102 kg/m3and 1 atmosphere= 1.01 105 N/m2)(a) 3.0 atm (b) 2.0 atm(c) 1.0 atm (d) 1.5 atm

13. In a thermodynamic process pressure of a fixedmass of a gas is changed in such a manner thatthe gas releases 20 J of heat and 8 J of work isdone on the gas if the initial internal energy ofthe gas was 30 J. The final internal energy will be(a) 36 J (b) 15 J(c) 18 J (d) 9 J

14. A carnot engine working between 300 K and600 K has work output of 800 J per cycle. Theamount of heat energy supplied to the enginefrom source per cycle will be(a) 800 (b) 1600(c) 1200 (d) 900

15. Calculate the energy radiated per minute fromthe filament of an incandescent lamp at 2000 K ifthe surface area is 5 105 m2 and its relativeemittance is 0.85, s = 5.7 108 MKS units.(a) 1230 J (b) 2215 J(c) 2115 J (d) 2325 J

16. An object is cooled from 75C to 65C in 2minutes in a room at 30C the time taken to coolthe same object from 55C to 45C in the sameroom (in minute) is(a) 7 (b) 6(c) 5 (d) 4

17. A satellite of mass m goes round the earth alonga circular path of radius r, let me is the mass ofthe earth and Re its radius. Then the linear speedof the satellite depends on

3(a) me, and r (b) me only(c) , me, V (d) me, Re and r

18. The equivalent capacitance in the given circuit is

3 Fm 3 Fm1.5 Fm

1.5 Fm(a) 3 F (b) 1.5 F(c) 2 F (d) 1 F

19. The rope shown at an instant is carrying a wavetravelling towards right created source vibratingat a frequency n consider the followingstatement:

a b c d e

(i) The speed of the wave is 4n ab(ii) The medium at a will be in the same phase

as d after 4 sec

3n(iii) the phase difference between b and e is

32p .

Which of these statement(s) is/are correct?(a) (iii) only (b) (i) and (iii) only(c) (ii) only (d) (ii), (i), (iii)

20. Which one of the following is the graph betweenfrequency v of the incident radiation andstopping potential?

21. Which transition emits light of lower frequency?(a) n = 6 to n = 2(b) n = 2 to n = 1

(c) n = 2 to n = 6(d) n = 1 to n = 2

22. Which one of the following is the weakest force?(a) Electrostatic force(b) Nuclear force(c) Electromagnetic force(d) Gravitational force

23. Work function of three metals A, B, C are 4.5 eV,4.3 eV, 3.5 eV respectively. If a light of wavelength4000 is incident on the metals, then(a) photoelectron are emitted from C(b) photoelectrons are emitted from A(c) photoelectron are emitted from B(d) photoelectron will not emitted from all the

surfaces24. The two masses m1

and m2 are joined by a springas shown. The system is dropped to the groundfrom a height. The spring will be

m1

m2(a) neither compressed nor stretched

regardless of the value of m1 and m2(b) neither compressed nor stretched only

when m1 = m2(c) stretched when m2 > m1(d) compressed when m2 < m1

25. Which of the following distance time graphrepresents one dimension at uniform motion?

(a) (b)

(c) (d)

26. Which logic gate is represented by followingdiagram?

4(a) XOR (b) NOR(c) OR (d) AND

27. A 220 V, 50 Hz AC source is connected to ainductance of 0.2 H and resistance of 20 W inseries. The current in the circuit is(a) 3.33 A (b) 33.3 A(c) 10 A (d) 5 A

28. The following figures (a) to (d) show variationof value by change of pressure. A gas is takenalong the path ABCDA. The change in internalenergy of the gas will be minimum in

A B

CDP

V

(a)(0, 0)

A B

CDP

V(b)

AB

CDP

V(c)

A B

CDP

V(d)

29. A toy car travels in a horizontal circle of radius2a, kept on the track by a radial elastic string ofunstretched length a. The period of rotation isT. Now the car is speeded up until it is moving ina circle of radius 3a. Assuming that the stringobeys Hook's law then the new period will be

(a)4T3

(b)2

33

T3

(c)3

T2

(d) 3 T4

30. We have a galvanometer of resistance 25W. It isshunted by a 2.5W wire, the part of total currentthat flows through the galvanometer is given as

(a)0

i 4i 11

= (b)0

i 3i 11

=

(c)0

i 2i 11

= (d)0

i 1i 11

=

31. When the key is pressed at time t = 0 then whichof the following statement about the current i inthe resistor AB of the given circuit is true

1000

1000

W

W

2V K A B

C1 Fm

(a) At t = 0, i = 2mA and with time it goes to 1mA

(b) i oscillates between 1 mA and 2mA(c) i = 2 mA at all t(d) i = 1 mA at all t

32. Eight drops of equal size are falling through airwith steady velocity of 10 cm/sec. If the dropscoalesce, what could be its terminal velocity?(a) 40 cm/sec (b) 20 cm/sec(c) 25 cm/sec (d) 50 cm/sec

33. Light of two different frequency whose photonhave energies 1 eV and 2.5 eV respectivelysuccessively illuminate a metal of work function0.5 eV. The ratio of maximum speed of the emittedelectron will be(a) 1 : 1 (b) 1 : 2(c) 1 : 4 (d) 1 : 5

34. A man is standing on a railway platform listeningto the whistle of an engine that passes the manat constant speed without stopping. If the enginepasses the man at time t0. How does the frequencyf of the whistle as heard by the man change withtime ?

(a) (b)

5(c) (d)

35. By opening the door of a refrigerator which isinside a room, the temperature of room(a) first decreases then increases(b) remains unchanged(c) increases(d) decreases

36. A vessel has 6 g of oxygen of pressure P andtemperature 400 K, a small hole is made in it sothat oxygen leaks out. How much oxygen leaksout if the final pressure is P/2 and temperature is300 K ?(a) 3 g (b) 2 g(c) 4 g (d) 5 g

37. The maximum acceleration of the body executingS.H.M. is a0 and maximum velocity is v0 theamplitude is given by

(a)0 0

1a v

(b)2

0

0

av

(c) v0a0 (d)2

0

0

va

38. Different voltage are applied across a p-njunction and the currents are measured for eachvalue. Which of the following graphs is obtainedbetween voltage V and current i

39. Which of the following graph represents thevariation of activity A of a radioactive substance

with time t?

A

t(a)

A

t(b)

A

t(c)

A

t(d)

40. Which one of the graphs represents thevariation of electric field strength E with distancer from the centre of a uniformly chargedconducting sphere ?

E

r(a)

R

E

r(b)

R

E

r(c)

R

E

r(d)

RCHEMISTRY

41. Heat2(s) (aq)MnO 4HCl+

2(aq.) 2 2MnCl 2H O Cl (g)+ +The equivalent weight of MnO2 in the abovereaction is :(a) 23.4 (b) 33.6(c) 43.5 (d) 53.6

42. Tetraethyl lead is used as :(a) Fire extinguisher(b) mosquito repellent(c) Petroleum additive(d) none of the above

43. 4 mole of A are mixed with 4 mole of B so, 2 molesof C are formed at equilibrium according to

6following. reaction, A B C D+ + . The valueof equilibrium constant is :

(a) 1 (b) 4 (c)14 (d)

12

44. The vapour pressure of benzene at a certaintemperature is 200 mm Hg. At the sametemperature the vapour pressure of a solutioncontaining 2 g of non volatile non electrolyte solidin 78 g of benzene is 195 mm Hg. The molecularweight of solid is :(a) 20 (b) 40 (c) 60 (d) 80

45. The metal not present in hard water is :(a) Ca (b) Na(c) Mg (d) Fe

46. At 300 K, the ratio of the average molecular kineticenergy of UF6 to that of H2 is(a) 2 : 7 (b) 7 : 2(c) 6 : 2 (d) 1 : 1

47. Graphite and diamond are :(a) polymorphs(b) allotropes(c) different crystal structure(d) all of these

48. The correct alternate for the cells spontaneousreaction is :(a) E0 cell should be infinite(b) E0 cell should be zero(c) E0 cell should be +ve(d) E0 cell should be ve

49. The maximum amount of sulphur is given by :

(a) 29spAgS(K 6 10 )-=

(b) 27spCuS(K 4 10 )-=

(c) 28spPbS(K 8 10 )-=

(d) ZnS (Ksp= 8 1030)

50. The highest electronegative element is :(a) carbon (b) oxygen(c) fluorine (d) nitrogen

51. Bromine can be liberated from KBr solution bythe action of :(a) chlorine (b) NaCl(c) KI (d) Iodine solution

52. The correct order of electron affinities of S, N, Oand Cl is :

(a) O = Cl < S = N (b) O < S < SI < N(c) N < O < S < Cl (d) O < N < Cl < S

53. In isotones the atomic number and mass numbersare :(a) same (b) different(c) equal (d) zero

54. The interhalogen compound not obtained is :(a) ICl (b) IF5(c) BrF5 (d) BrCl7

55. The element prepared by electrolysis is :(a) sodium (b) chlorine(c) fluorine (d) bromine

56. The element chlorine consists of mixture of75.53% 17Cl

35 and 24.47% 17Cl37 having a mass

of 34.97 amu and 36.95 amu, respectively. Theatomic weight of chloride is :(a) 35.25 (b) 35.45(c) 36.25 (d) 36.45

57. The solubility of Ag2S is [Ksp = 256 106] :

(a) 4 102 (b) 4 103(c) 0.4 102 (d) 0.4 103

58. Marsh gas contains :(a) C2H4 (b) C2H6(c) C2H2 (d) CH4

59. Vitamin B12 contains :(a) Cu (b) Fe(c) Mg (d) Co

60. 720 g of water contains moles of water :(a) 20 (b) 40 (c) 60 (d) 80

61. Nitroalkane which do not exhibit tautomerism is:(a) 3 -nitroalkane (b) 2-nitroalkane(c) 1-nitroalkane (d) all of these

62. The paramagnetic element is :(a) Ni2+ (b) Sc3+(c) Cu+ (d) Zn2+

63. Addition of HBr on propene produce :(a) CH3CH2CH2Br (b) CH3BrCH2CH3(c) 3 3

|CH CH CH

Br

(d) none of these

64. Which of the following is not a planar compound?(a) C2H2 (b) NH3(c) N2O (d) None of these

65. The rate constant of third order reaction is :(a) mol lit1 s1 (b) mol2 L2 T1(c) mol1lit s1 (d) mol2 lit1s1

766. By the reduction of carbonyl compounds thealcohol not obtained is :(a) primary alcohol(b) secondary alcohol(c) tertiary alcohol(d) all the above

67. The mixture of gases used for asthma patients is(a) O2 + He (b) O2 + Ne(c) O2 + H2 (d) O2 + Ar

68. Acetate ion have :(a) two carbon, oxygen double bond(b) two carbon, oxygen single bond(c) one carbon, oxygen single bond and one

carbon, oxygen double bond(d) none of these

69. The difference between energy of product andenergy of reactant is called :(a) entropy (b) heat content(c) heat of fusion (d) activation energy

70. The most covalent bond is :(a) C S (b) C O(c) C F (d) C Br

71. A solution is made up of 10 ml of 0.1 NaOH and10 ml of 0.05 N H2SO4. The pH of solution is(a) 7 (b) > 7(c) < 7 (d) none of these

72. The addition of 1% alcohol to chloroform acts as a :(a) positive catalyst (b) negative catalyst(c) autocatalyst (d) none of these

73. (s) (aq) (s) (aq)Zn Cu Cu Zn++ +++ +

The E.M. E of above reaction is 1.10 volt at 25C.What is EMF of cell when [Cu++] = [Zn++] = 0.1M(a) 1.10 volt (b) 1.10 volt(c) 0.110 volt (d) 0.110 volt

74. The colour of iodine solution is discharged byshaking it with aq. solution of :(a) sodium sulphite(b) sulphuric acid(c) sodium sulphate(d) sodium thiosulphate

75. The entropy change (DS) in a system increasesas :(a) solid < liquid < gas(b) liquid < gas < solid(c) solid < gas < liquid

(d) gas < solid < liquid76. The element having maximum hydration energy

is :(a) Na (b) K(c) Rb (d) Cs

77. Modern periodic table is based on atomic numberof the elements. The significance of atomicnumber was proved by the experiment of :(a) Discovery of X-ray by Roentgen(b) Mullikens oil drop experiment(c) Braggs work on X-ray diffraction(d) Mosleys work on X-ray spectra

78. The shape of XeO4 molecule is tetrahedral due to(a) sp (b) sp2(c) sp3 (d) none of these

79. Iodoform test is given by(a) 1- propanol (b) Methanol(c) 2 - butanol (d) 1- butanol

80. 0.3 M H3PO3 shows the normality of(a) 0.3 (b) 0.6(c) 0.9 (d) 0.1

MATHS

81. If L1 = 0 and L2 = 0 be two intersecting straightlines, the number of points, whose distance fromL1 is 2 units and from L2 is 5 units is(a) one (b) zero(c) four (d) infinite

82. If the length of a focal chord of parabola y2 = 4x

is 254

and has positive slope, then the slope will

be

(a) 3 (b)3

1

(c) 34

(d) 1

83. Let a i j k= + +ur

, c is a vector such that

a . c | c |=ur ur ur

, | a c | 6+ =ur ur

then c.a is equalto(a) 1 (b) 5(c) 3 (d) None of these

884. Let a , b and cur ur ur

be three non-coplanar vectors

and d be a non-zero vector, which is ^ to

(a b c )+ +ur ur ur

. Now if

d sin x(a b ) cos y(b c ) 2(c a )= + + ur ur ur ur ur ur ur

, then minimum value of x2 + y2 is equal to(a) p2 (b) 0

(c)4

2p(d)

45 2p

85. If

.....CxBxAxsin1excosxsinxcos)x1ln(xtanx2sine

)x( 22x2

2x

+++=-

+=D

then B =(a) 0 (b) 1(c) 2 (d) None of these

86. The curve xy = c (c > 0) and circle x2 + y2 = 1touch at two points, then distance betweenpoints of contacts is(a) 1 (b) 2(c) 2 2 (d) 4

87. If 2 4x cos y cos cos3 3p p q = q + q +

,

then value of xy + yz + zx is(a) 1 (b) 0(c) 2 (d) 3

88. If in a =D 90C,ABC then value of tan(A B) is

(a)ab2

ba 22 +(b)

ab2|ba| 22 -

(c)4c

2ab(d)

ca2b

89. The value of integral

-+ ---1

0211

1dx

xx2cosxsin

xsin is

(a) 1 (b)21

(c) 2 (d) 090. Coefficient of x25 in the expansion of expression

rnr50

0rr

50 )x2()3x2(C -

=-- is

(a) 50 25C (b)50

24C-

(c) 50 25C- (d) 50 30C-91. The orthocentre of the triangle formed by the

points A (iz+z), B(z iz), and C(0) is(a) 0+0i (b) 1+i(c) 2+i (d) 3+2i

92. If a, b, c are in G.P., or (x a) is a factor of ax2 +2bx + c, then value of the determinant

0cbbacbcbbaba

+a+a+a+a

is equal to

(a) 1 (b) 1(c) 2 (d) 0

93. The value of

p

6f where

( )0cossin

cossinsincossinsincoscos

f 22

q-qqqqqq-qqq

=q

(a) 0 (b) 1(c) 2 (d) 3

94. The equation x3 + 5x2 + px + q = 0 and x3 + 7x2 +px + r = 0 have two roots in common. If their thirdroots are x1 and x2, then (x, x2) =(a) (5, 7) (b) (5, 7)(c) (5, 7) (d) (5, 7)

95. Let P(x) = 0 be the polynomial equation of leastpossible degree with rational coefficients having

33 497 + as the root. Then the product of allroots of P(x) = 0 is(a) 56 (b) 42(c) 343 (d) 7

96. A class contains three girls and four boys. EverySunday five students go on a picnic, a differentgroup being sent each week. During the picnic,the class teacher gives each girl in the group adoll. After all possible groups of five have goneonce, the total number of dolls which the girls

9have got is(a) 27 (b) 11(c) 21 (d) 45

97. The roots of the equation x5 40x4 + px3 + qx2 +rx + s = 0 are in geometric progression and thesum of their reciprocal is 10. Then |S| is equal to(a) 64 (b) 16(c) 32 (d) None of these

98. A truck is to be driven 300 km on a highway atconstant speed of x km/h. Speed rules of highwayrequire that 60x30 . The fuel costs Rs.10

per litre and is consumed at rate of

+

600x2

2

litres per hour. The wages of driver are Rs.200per hour. The most economical speed is (km/h)(a) 30 (b) 60(c) 20 (d) 40

99. Let )1n(n)1n2(1

823r4r6r2

)r(

32

++-=D , then value

of =

Dn

1r

)r( will be equal to

(a)6

)1n2(n2 +(b)

2)4n3)(1n2(n ++

(c)12

)1n(n 33 +(d) Zero

100. If the function f(x) = sin1(x) and g(x) = xsec 1-

then domain of the f og (x) is(a) [0, 1] (b) [1, 2](c) [1, sec 1] (d) [1, )

101. The number of solutions, which lie in the interval0 2 q p , of the equation

2cos 3cos 2 0q - q + = is(a) 3 (b) 4(c) 5 (d) 2

102. The complete solution set for sin1(x)= 3 sin1 (a) is

(a)21a0 (b) 0a

21 -

(c)21a

21 - (d) None of these

103. The curve y = x + sin x has(a) No maximum point(b) Some maximum points(c) Some minimum points(d) None of these

104. =p

p

3

6

x2sindx

(a) 3log21

e (b) 3loge

(c) 3log2 e (d) None of these

105. If in the expansion of m)x1( + n)x1( , the

coefficients of x and 2x are 3 and 6respectively, then m is(a) 6 (b) 9(c) 12 (d) 24

106. The greatest value assumed by function f(x) = 5 |x 3| is(a) 3 (b) 8(c) 5 (d) 2

107. Two circles (x 1)2 + (y 3)2 = r2 and x2 + y2 8x+ 2y + 8 = 0 intersect in two distinct points if(a) 2 < r < 8 (b) r < 2(c) r = 2 (d) r > 2

108. The value of dxx30x30log

3

33

3

-

+-

is

(a)3 3

30

30 x2 log30 x

- + (b) 57

3log

(c)3

57log (d) 0

109. Let f(x) be a function and 2n > a letn

1a n

x f (x(a x)) dx-

= -I and

10

n

2a n

f (x(a x)) dx-

= -I then 2

1

II =

(a)n2

(b) 2a

(c)12

(d)a2

110. The common tangent to the curve y = sin x andy = x2 + x is(a) y = x (b) y = x + 1(c) y + x+ 2 = 0 (d) y = x

111. Domain of the function f(x) = sin1 [1 + cos x] +

2x16 - ( [ ] denotes greatest integerfunction) is(a) [4, 4] {0} (b) (4, 4)(c) [0, 2p] (d) [0, p]

112. The number of common tangents that can bedrawn to the circle x2 + y2 4x 6y 3 = 0 and x2+ y2 + 2x + 2y + 1 = 0(a) 1 (b) 2(c) 3 (d) 4

113. Two lines are given by (x 2y)2 + k (x 2y) = 0.The value of k so that distance between them is

(a) k = 0 (b) k = 53(c) k = 5 (d) k = 3

114. Two independent events A1 and A2 withprobability of happening p1 and p2, what is theprobability that atleast one of them happens(a) p1 + p2 (b) p1 p2

(c) p1 + p2 p1p2 (d)1 2

1 2

p pp p+

115. A dice is thrown 7 times. The chance that an oddnumber turn up exactly 4 times

(a) 12871

(b) 12893

(c) 12835

(d) None of these

116. If a coin is tossed n times, the probability thathead appears odd no. of times is

(a) n21

(b) 1n21-

(c)21

(d) None of these

117. If y1

1xx)x(f =-

= , then f(y) =

(a) x (b) x 1(c) 1 x (d) 1 + x

118. The area bounded by the curves y2 x = 0 and y x2 = 0 is

(a) 37

(b) 31

(c) 35

(d) 1

119. Solution of differential equaiton

x2xsindxdy += , is

(a) y = x2 cos x + c (b) y = cos x + x2 + c(c) y = cos x + 2 (d) y = cos x + 2 + c

120. If z = x + iy and w = )iz()iz1(

--

, then | w | = 1, shows

that in complex plane(a) z is situated on imaginary axis(b) z is situated on real axis(c) z is situated on unit circle(d) None of these

121. Four points (0, 4, 3), (1, 5, 3), (2, 2, 1) and(1, 1, 1) lie on the plane, whose equation is(a) 4x + 3y + 2z 9 = 0(b) 9x 5y + 6z + 2 = 0(c) 3x + 4y + 7z 5 = 0(d) none of these

122. Function f(x)=

-

11

(b) 0CzByAx 111 =++(c) 0czbyax 111 =++(d) 0CcBbAa =++

124. The resultant of two forces P and Q acting at an

angle a is equal to (2m + 1) )QP( 22 + . Whenthe forces act at an angle (900- a ), the resultant

is (2m - 1) )QP( 22 + . Then value of tan a is:(a) (m - 1)/(m + 1) (b) (m + 1)/ (m - 1)(c) m (d) 1/m

125. If RR :f be a function defined by f (x) = 4x37. Then(a) f is one-one -into(b) f is many-one - into(c) f is many-one onto(d) f is bijective

ENGLISH PROFICIENCY

DIRECTIONS (Q. 126) : Choose the word which isnearest in meaning to the given word:126. TRANSGRESSOR

(a) Passenger (b) Law-breaker(c) Protector (d) Comrade

DIRECTIONS (Q. 127) : Choose the word which isnearly opposite in meaning to the given word:127. PREDILECTION

(a) Oblivion (b) Objectivity(c) Aversion (d) Defeat

DIRECTIONS (Q. 128) : The following questionsconsist of two words that have a certain relationshipto each other, followed by four alternatives. Selectthe best alternative that has same relationship as theoriginal pair of words.128. Crche : Infants

(a) School : Pupils(b) Deck : Sailors(c) Cottage : Guests(d) Aircraft : Crew

DIRECTIONS (Qs. 129-130) : Pick up the mosteffective word from the given words to fill in theblanks to make the sentence meaningfully complete.129. According to the weather __________ it is

going to be cloudy today.(a) announcement(b) indication(c) prediction(d) forecast

130. The villagers __________ the murder of theirleader by burning the police van.(a) protested (b) avenged(c) mourned (d) consoled

DIRECTIONS (Q. 131) : In this question, find outwhich part has an error.131. The police has (a)/ arrested the thief (b)/ who

broke int my house (c)/ last night (d)

DIRECTIONS (Q. 132) : Choose the word that bestdefines the given phrase:132. Able to use both hands alike

(a) Dexterous (b) Ambidextrous(c) Skilful (d) Expert

DIRECTIONS (Q. 133) : In question below, a part ofthe sentence is underlined. Below are givenalternatives to the underlined part at (a), (b), (c)which may improve the sentence. Choose the correctalternative. In case no improvement is needed, youranswer is (d). Mark your answer in the Answer Sheet.133. She is quite well now, except a slight cold.

(a) except have a slight cold(b) excepting a slight cold(c) except for a slight cold(d) No improvement

DIRECTIONS (Q. 134) : In question below fouralternatives are given for the Idiom / Phraseunderlined in the sentence. Choose the alternativewhich best expresses the meaning of the Idiom/Phraseand mark it in the following options.134. The police cordoned off the area after the

explosion.(a) The police checked everyone in the area(b) The police did not allow anyone to leave

the area(c) The police filled the whole area(d) The police isolated the area

DIRECTIONS (Q. 135) : In question below, a part ofthe sentence is underlined. Below are givenalternatives to the underlined part at (a), (b), (c)which may improve the sentence. Choose the correct

12

alternative. In case no improvement is needed, youranswer is (d).Mark your answer in the followingoptions.135. She is quite well now, except a slight cold.

(a) except have a slight cold(b) excepting a slight cold(c) except for a slight cold(d) No improvement

DIRECTIONS (Qs. 136-137) : In questions below,the 1st and the last sentences/parts of the passage /sentence are numbered 1 and 6. The rest of thepassage / sentence is split into four parts and namedP, Q, R and S. These four parts are not given in theirproper order. Read the passage/sentence and findout which of the four combinations is correct. Thenfind the correct answer.136. 1. There are a lot of ways to communicate :

speaking, singing, clapping, hooting.P. Even animals communicate with one

another.Q. Only humans can express their thoughts

and feelings in words because of oursuperior brain.

R. Both humans and animals alsocommunicate through body language.

S. But their ways differ from the humans.6. Sometimes we dont use words but make

gestures (like traffic signs) or simplemovements of the hand in order tocommunicate.

(a) PRSQ (b) QPRS(c) PQRS (d) PSQR

137. 1. Fires in the Steppes or bushes scaredhumans earlier.

P. Gradually, they learnt to appreciate thepower of fire.

Q. It gave them light and warmth and keptaway wild animals.

R. About 700,000 years ago, humans startedfire accidentally by lightning.

S. They could harden the tips of woodenspears and cook meat in it.

6. Soon they learnt to produce fire by strikingflintstone and pyrite with each other or byrubbing lumbers.

(a) QSPR (b) PQSR(c) PQRS (d) QRSP

DIRECTIONS (Qs. 138-140) : Read the followingpassage carefully and answer the questions given

below it:And then Gandhi came. He was like a powerful currentof fresh air that made us stretch ourselves and takedeep breaths, like a beam of light that pierced thedarkness and removed the scales from our eyes, like awhirlwind that upset many things but most of all theworking of peoples minds. He did not descend fromthe top; he seemed to emerge from the millions of India,speaking their language and incessantly drawingattention to them and their appalling condition. Getoff the backs of these peasants and workers, he toldus, all of you who live by their exploitation; get rid ofthe system that produces this poverty and misery.138. Gandhi came like a powerful current of fresh air

and(a) awakened us to the plight of the masses in

the grip of oppressors(b) made us patriotic(c) emboldened us to attack and destroy the

oppressors(d) praised our culture

139. The rise of Gandhi(a) shocked people(b) made India powerful(c) made the condemnation of the exploiter

final(d) made women feel secure

140. Gandhi fought the(a) rich (b) oppressor(c) apathetic masses (d) unjust system

LOGICAL REASONING

DIRECTIONS (Qs. 141-142) : In question belowselect the related word/letters/number from the givenalternatives.141. MOQS : ACEG :: PRTV : ?

(a) KMNP (b) OQSU(c) EGIJ (d) FHJM

142. Swimming : River : : Hiking : ?(a) Mountain (b) Sea(c) Road (d) Pond

DIRECTIONS (Q. 143) : In question below, find theodd words /letters / number pair from the givenalternatives. .143. (a) KHEB (b) WTQN

(c) MKHE (d) MIDADIRECTIONS (Q. 144) : In question below, a series

13

is given, with one term missing. Choose the correctalternative from the given ones that will completethe series.144. 2, 8, 18, 32, 50, ?

(a) 70 (b) 68(c) 64 (d) 72

145. Select the missing number from the givenresponses:

5

12110

54

?

26

(a) 132 (b) 122(c) 222 (d) 212

DIRECTIONS (Q. 146) : In below question these isan incomplete Figure and four Answer Figures. Astudent has to select one diagram from the AnswerFigures which fits into the blank column inincomplete Figure in order to complete it:

146.

?

Incomplete Figure

Answer Figures

(a) (b) (c) (d)

DIRECTIONS (Q. 147) : In following question, selectthat combination of parts (A), (B), (C), (D) and (E)which if fitted together will form a square.

147.

(A) (B) (C) (D) (E)

(a) ACD (b) ABD(c) BCD (d) CDE

148. A piece of paper is folded and cut/punched asshown below in the question figure. From thegiven answer figures, indicate how it will appearwhen opened.Question figures:

Answer figures:

(a) (b) (c) (d)149. Select the figure that is missing from the

collection below:

?

(a) (b)

(c) (d)

DIRECTIONS (Q. 150) : In these tests find the oddfigure out:

150.

(a) (b) (c) (d)

14

HINTS & SOLUTIONS

PHYSICS1. (d) Magnitude of magnetic field along AB is

constant and its direction is same every

where on AB as B = 0 I2r

2. (a) Ionisation potential for H2 = 13.6V

Ionisation energy En = 213.6n

eV..

For ground state n = 1\ Ep = 13.6 eV

For 2nd excited state n = 2

\ Ep = 213.6 13.6

42= = 3.4 eV..

3. (d) All the three processes mentioned canproduce visible light depending on thefrequency of the radiation emitted by theprocesses.

4. (d) With the increase in frequency, XL = 2pvLincreases.

Phase angle, cos f = LXR

\ cos f increases.\ f first decreases till 90 and then increases.

5. (c) wateroil

sin i 1.33sin r 1.45

= =

sin 40 1.33sin r 1.45

=

0.6428 1.33sin r 1.45

=

sin r = 0.6428 1.451.33

sin r = 0.7007 = sin 44.5 r = 44.5

6. (a) For deviation with out dispersions (Achromatic combination)

1V 1R2

1 2V 2R

AA

-= - -1.523 1.515 0.0081.616 1.650 0.034

-= =- = 0.2353A2 = 10 (0.2353) = 221'11'' 2.35

7. (b) For convex lens,

1 2

1 1 1( 1)f R R

= - - R1 = 20 cm, R2 = 20 cm.

= (1.5 1) 1 120 20

+

= 1 2 1 1 12 20 2 10 20 = =

f = 20 cm = 0.2 mFor water lens,R1= (for plane surface)R2 = 20 cm.1 4 1 1 1 1 1

1f ' 3 20 3 20 60

- - = - - = = -f ' = 60 cm = 0.60 m

8. (b)FA

= 106 N/m2, r = 3 103 kg/m3, l = ?F = mg = l pr2 rg = l A rg

Stress, F gA

r= l

l = 6

3F / A 10 100

g 33 10 10r= =

= 33.33 m.

9. (a) S = 7 102 N/m,r = 0.1mm = 0.1 103mF = mg

S l = mg mg = S 2pr\ Weight of water

= 7 102 2 322

0.1 107

- = 44 106 N

10. (d) r = 0.3 mm = 0.3 103mVT = 1 m/sh = 18 105 poise = 18 106 decapoiseViscous force, F = 6phrVT

= 6 227

18 106 0.3 103 1

= 101.73 109 N

15

11. (d) Average K.E = 3 RT2

At 0C, average K.E = 3

R 2732

[T = (0 + 273)K]At 273C,

average K.E = 3

R (273 273)2 +

= 3

R2 2 273

\ Ratio = 212. (a) R.M.S speed of H2 = 3180 m/s

H2r = 8.99 102 kg/m3,1atm = 1.01 105 N/m2

Pressure, P = 21

c3

r

= 2

51 8.99 10 3180 31803 1.01 10

- atm

= 3 atm13. (c) dQ = 20 J, dW = 8 J, U1 = 30 J

By 1st law of thermodynamics,dQ = dU + dW

dU = dQ dW= 20 + 8 = 12 JFinal internal energy, U2 = U1 + dU= 30 12 = 18 J

14. (b) Temperature of source, T1 = 600 K,Temperature of sink,T2 = 300 K, W = 800 J/cycle.

Efficiency, h = 1 21

TT

= 1 300 1600 2

=

Also, h = 1

WQ

Q1 = W 800

1/ 2h = = 1600 J15. (d) T = 2000K, A = 5 105m2, e = 0.85

s = 5.7 10 8 MKS unit.Energy radiated/sec = AesT4= 5 105 0.85 5.7 108 (2000)4= 5 0.85 537 1013 1012 16= 387.6 101Energy radiated/minute = 38.76 60= 2325.6 J

16. (d) Rate of cooling,

dTdt

= K(T T0) dT2

= K(70 30)

dTK

= 40 2 = 80

\ dTdt '

= K(50 30)[In both cases, dT is same]

dt' = dT 1 80K 20 20

= = 4 min.17. (d) Linear speed of the satellite

v = e eGm Gm

r R h= +

[h =height of the orbit above the surface]\ v depends on me, Re and r

18. (d) Two 1.5 F capacitors are in parallel\ Cp = 1.5 + 1.5 = 3F

Three 3F capacitors are in series.

\eq

1 1 1 1 3C 3 3 3 3

= + + = = 1

\ Ceq = 1F19. (a) Statement (iii) is only correct as the phase

differences between points b and c, c and d

and d and e are 2p

each

\ The phase difference between b and e

= 3

2 2 2 2p p p p+ + =

20. (b)

V0

n0n

The intercept on the x-axis denotesthreshold frequency (v0)

21. (a) The frequency of the radiation decreasesand wavelength increases as it goes from ahigher state to lower state. n = 6 to n = 2 willgive light of lowest frequency and highestwavelength

22. (d) Gravitational force is the weakest force andhaving longest range as it exists betweenany two bodies in the universe.

23. (d) WA = hv0A = 4.5 eV, hv0B = 4.3 eV,hv0C = 3.5eV.

E = hv =34 8

7 19hc 6.6 10 3 10

4 10 1.6 10l-

- - =

= 3.09 eV.

16

\ The energy of the photon is less than thework function of all 3 metals, so photoelectron will not be emitted from all threesurfaces.

24. (d) If m2 < m1 then the K.E of m1 will be morethan m2, so to balance the spring will getcompressed.

25. (a) In one dimension at uniform motion equaldistance is travelled at equal intervals oftime. So, velocity is constant and henceacceleration a = 0

26. (d)AB Y

This represents AND gate.Output Y = AB

27. (a) V = 220 V, v = 50 Hz, L = 0.2 H, R = 20 WXL = 2pvL = 2 3.14 50 0.2= 100 0.628 = 62.8WZ = 2 2 2 2LX R (62.8) 20+ = +

I = V 220Z 43473.84= = 3.33A

28. (b) The change in internal energy will beminimum in fig. (b) as the area of a circle isminimum.

29. (c) T = 2mv

k.xr

=mw2r = kx

Initially, w2 = kx ka kmr m(2a) 2m

= = ...(i)

Secondly, w'2 = k(a) km(3a) 3m

= ...(ii)

\2' k / 3m 2

k / 2m 3ww

= =

22 / T ' 2

2 / T 3pp

=

or T 2T ' 3

=

3T ' T2

=

30. (d) G = 25 W, S = 2.5 W

We have, ig = 0 0S 2.5

i iG S (25 2.5)

=+ +

0 02.5 1i i27.5 11

= =

\0

i 1i 11

=

where I current through galvanometerI0 Total current.

31. (a) At t = 0, capacitor C will produce reactance

Xc = 61 1C 50 10w -=

\ 6eq

1 50 1R 100010

= +

= 1.05 103 or Req = 952.4Total resistance = (1000 + 952.4)= 1952.381 W

\ I1 = 2

1952.381= 1.0244 mA

At t > 0, capacitor C will be cut off circuit.Req = 1000 + 1000 = 2000 W

I2 = 2

2000= 1 mA

\ at t = 0, i = 1.024 mA and with time it goesto 1 mA

32. (a) Terminal velocity, vT = 22 r ( )g

9r s

h-

\ vT r2

\2

T2

T

v rv ' R

= (i)Now, Volume of the big drop = 8 volumeof each small drop

3 34 4R 8 r3 3

p p= R = 2r

\2 2

2 2T

10 r rv ' (2r) 4r

= = [using equation (i)] v'T =40 m/s

33. (b) hv1 = 1 eV, hv2 = 2.5 eVhv0 = W = 0.5 eV

We have, 21

mv2

= hv W = hv hv0

\2

1 012

2 02

h hvh hv

-= -v vv v

= 1 0.5 0.5 5 12.5 0.5 2 20 4- = = =-

Ratio of v1and v2 = 1 : 2

17

34. (b) When the train approaches to the observerthe observed frequency increases,becomes maximum and when it passes theobserver it becomes zero.

35. (c) When the door of a refrigerator is openedthe temperature of the room increases asthe room is acting as the source here wherethe heat is rejected.

36. (c) Here, 1 21 1 2 2

P Pn T n T

=

P1 = P, P2 = P/2, n1 = 6

16, n2 =

m16

T1 = 400K T2 = 300K

\ P P / 26 m400 300

16 16

=

m = 4g37. (d) Max. acceleration in S.H.M , a0= w2a .....(i)

[a = amplitude]max. velocity = wav0 = wa

v02 = w2a2 ......(ii)

\ (ii)(i)

a = 20

0

va

38. (b) For p-n junction diode in forward bias, thecurrent first increases and then becomesmaximum, whereas in reverse bias itincreases slowly in opposite direction.

39. (a) Activity is defined as the rate ofdisintegration of the substance i.e.,A = A0 e

lt

Where A0= Activity at t = 0A= Activity after time tActivity of a radioactive element decreaseswith time and it is an exponential function,so graph (a) is correct.

40. (a) In a uniformly charged conducting sphere,electric field inside the sphere is zero.Outside it decreases uniformly, so graph(a) is correct.

CHEMISTRY

41. (c) 2 2 2 2MnO 4HCl MnCl 2H O Cl+ + +1 mole = M 71 gQ 71 g of 2Cl is displaced by

= 1 mole (M) of 2MnO\ 35.5 g of 2Cl is displaced by

= M M35.571 2

= of MnO2\ Equivalent weight of 2MnO

= Molecular mass

2 = 87 43.52

=42. (c) Tetraethyl lead is used as petroleum additive

to prevent knocking of engine.43. (a) A B C D+ +

Initial conc. 4 4 0 0Equilibrium conc. (4 2) (4 2) 2 2

Let volume = VL = 2

C[C] [D]k[A] [B]

= = 2 / V 2 / V2 / V 2 / V

= 1

44. (d) Given p = 200 mm Hgp = 195 mm Hgw = weight of solute = 2gW = weight of solvent = 78 gM = Molecular weight of solvent (benzene) = 78m = Molecular weight solute = ?p p w M

p W m - =

or200 195 2 78

200 78 m- =

or 5 2200 m

= \ m = 8045. (b) The hardness of water is due to sulphate

carbonates and chlorides of Ca and Mg.\ Na is not present in hard water.

46. (d) Average molecular K.E = 3 KT2

It means kinetic energy depends on T only

Q Temperature of 2H and 6UF both issame,\ Ratio of average molecular K.E = 1 : 1

47. (d) Graphite and diamond are allotrops ofcarbon.Graphite and diamond are polymorphsbecause they differ in arrangements inatoms in crystals.

48. (c) The cell reaction is spontaneous only whenE cell is positive.

49. (b) More the value of spk , greater will be

amount of sulphur obtained.\ Amount of sulphur obtained from CuSwill be greatest among given choices.

18

50. (c) Electronegativity is the tendency to attractshared pair of electron towards itself.Fluorine has highest electron affinity amongall elements of periodic table.

51. (a) 2Br is liberated from KBr solution by action

of 2Cl because 2Cl is more electronega-tive than bromine.

52. (c) Electron affinity is the tendency is attractshared pair of electron towards itself. Itsvalue decreases in a group and increasesin a period. The correct order of electronaffinities is as follows N < O < S < Cl

53. (b) Isotones are atoms of different elementshaving same member of neutrons butdifferent atomic number and atomic mass.

54. (d) The interhalogens are compounds formedby reaction of halogens among themselves.The more electronegative halogen formsanion and more electropositive halogenforms cation. The difference betweenelectronegativity of Br and Cl is too less.So BrCl7 is not formed.

55. (c) Fluorine is prepared by electrolysis of aq.

2KHF .

56. (b) Given - 3517Cl 75.53% and mass of Cl34.97 amu

3717 C - 24.47% and mass of Cl 36.95 amu

\Atomic weight of chlorine

=(75.53 34.97) (24.47 36.95)

100 +

= 3545.45

100= 35.45

57. (a) Let solubility of 2Ag S = x moles /L

2Ag S 2Ag S+ --+

\ 2spk [Ag ] [S ]+ - -= = 2(2x) (x)

\ 3spk 4x=Given 6spk 256 10

-=

or 6 3256 10 4x- =

or 6

3 256 10x4

-=

\ 2x 4 10-=

58. (d) 4CH is main constituent of Marsh gas.

59. (d) Vitamin 12B contains cobalt (Co).

60. (b) Given - mass of 2H O = 720 g

Moles of water = Mass of water

Molecular mass of water

= 72018

= 40 moles

61. (a) 3-nitro alkanes 2

R|

R C NO|R

- -

do not

have a -hydrogen atoms, so it does notexhibit tautomerism.

62. (a) The elements which have unpaired electronare paramagnetic.

2 2 6 2 6 2 8(G.S.)Ni 1s ,2s ,2p ,3s ,3p ,4s ,3d=2 2 2 6 2 6 0 8Ni 1s ,2s , 2p ,3s ,3p ,4s ,3d+ =

3d8

Q 2Ni + has two unpaired electrons.\ It is paramagnetic.

63. (c) The addition of HBr to propene takes placeaccording to Markownikoffs rule.According to this rule negative part ofreagent adds to carbon atom having lessernumber of hydrogen atoms.

3 2 3 3CH CH CH HBr CH CH CH|

Br

= + - -

64. (b) The 3NH has 3sp hybridisation and has

pyramidal structure. So, it is not planarcompound.

65. (b) Units of rate constant for nth order =1 1 n 1[(mol lit )] t- - -

For third order reaction n = 3

\Units are 1 1 3 1(mol lit ) t- - - = 2 2 1mol lit t- - -

66. (c) Aldehyde Reduction 1 alcohol

Ketone Reduction 2 alcohol\ 3 alcohol cant be prepared byreduction of carbonyl compounds.

19

67. (a) Mixture of oxygen and helium is used totreat patients of asthama.

68. (c) 3CH COO- 3

O|

CH C O

-

- =acetate ion\ It has 2 carbon atoms, one C-oxygenbond and one carbon and oxygen doublebond.

69. (b) Heat content or Enthalpy = Energy ofproducts Energy of reactants

70. (a) Lesser the difference betweenelectronegativities of bonded atoms, morewill be convalent character in bond.\ Among given choice C S bond is mostcovalent in nature.

71. (b) Milliequivalents of NaOH = 10 0.1 = 1

Miliequivalents of 2 4H SO = 10 0.05 = 0.5Q Mili equivalents of NaOH are in excess.\ Solution is basic in nature and pH > 7.

72. (b) Addition of 1% alcohol to chloroform actsas negative catalyst because it decreases

the rate of decomposition of 3CHCl .

73. (a) (aq) (aq)(s) (s)Zn Cu Cu Zn+ + + ++ +

Given [Cu ] 0.1+ + = , [Zn ] 0.1+ + =n = 2, 0cellE = 1.10 volt

0cell cell

.059 ZnE E logn Cu

+ +

+ + 0= -

= 0.059 0.11.10 log2 0.1

- =

0.0591.10 log12

-

= 0.0591.10 02

- = 1.10 V

74. (d) 2 2 3 2 2 4 6PurpleSodium ColourlessColouredthiosulphite

2Na S O I Na S O 2NaI+ +144424443

75. (a) Entropy is measurement of randomness.Gases have highest entropy. The correctorder of entropy is solid < liquid < gas.

76. (a) Smaller the size of atom or ion, greater willbe hydration and hydration energy.

\ Na has smallest size and greatest hydrationenergy among given choices.

77. (d) Modern periodic table is based on atomicnumbers and its significance was provedby the Mosleys work on X-ray spectra.

78. (c) Hybridisation

= No. of e + No. of mono + charge charge1 in valence valent on on

2 shell atom anion cation

For 4XeO

Hybridisation = 12

(8 + 0 + 0 0) = 4

\ 3sp hybridisation79. (c) Iodoform test is given by alcohols which

have 3

OH|

CH CH- group. On reaction with

2I and alkali they give yellow ppt. of CHI3

3 2 3

OH|

CH CH CH CH- - -2 - butanol

Only 2-butanol has 3

OH|

CH CH- groupamong given choices, so it gives iodoformtest.

80. (b) Molarity of 3 3H PO = 0.3 M;

Basicity of 3 3H PO = 2Normality = Molarity basicity = 0.3 2

= 0.6

MATHS81. (c) We can draw two parallel lines to L1 at a

distance of 2 units and 2 parallel lines to L2at a distance of 5 units and these 4 lines willintersect at 4 points.

82. (c) Length of focal chord will be

4251

t11t 2

2 =+++

25

t1t =+ 2t = . Since slope is

positive. Therefore t = 2.

The end points will be (4, 4),

-1,

41

.

Slope = 43 .

20

83. (a) 6|ca|c.a2|c||a|)ca.()ca( 222 =+=++=++

6|c|2|c||a| 22 =++

03|c|2|c| 2 =-+ 1|c| =84. (d) )cb(.d]cba[ycosa.d +-==

[as 0)cba(.d =++ ]

]cba[

)cb(.dycos +-= ; Similarly

]cba[

)ca(.d2and]cba[

)ba(.dxsin +-=+-=

sin x + cos y + 2 = 01ycos1xsin2ycosxsin -=-=-=+

Since we want minimum value of x2 + y2, so

x = p=p- y,2

.

85. (a)

x 2

2 x 2

e 2cos 2x 2x sec x'(x) ln(1 x) cos x sin x

cos x e 1 sin x

D = +-

x 2

2 x 2

e sin 2x tan x1 sin x cos x

1 xcos x e 1 sin x

+ -+

-x 2

2 x 2

e sin 2x tan xln(1 x) cos x sin x B 2Cx ....

2x sin x e 2x cos x

+ + = + +-Put x = 0,

0010010001

001101001

001010021

B =++=

86. (b) Since the two given curves touch eachother we have

0cxx01xcx 2242

22 =+-=-+

This equation will have equal roots iff (1)2

4c2 = 0 21c

41c2 ==

\ pts are

21,

21

and

--

21,

21

Roots of equation 041xx 24 =+- are

21y&

21x == ;

Clearly distance between points of contact= 2 units.

87. (b) Let

k3

4cosz3

2cosycosx =

p+q=

p+q=q

zk

34cos;

yk

32cos;

xkcos =

p+q=

p+q=q

2 4cos cos cos3 3p p q + q + + q +

k k k 0x y z

= + + = xy yz zx 0 + + =

88. (b) 1sec(A B)cos(A B)

- =-

21 1 cb a a bcos A cos B sin Asin B 2ab. .c c c c

= = =+ +

Now 2tan(A B) sec (A B) 1- = - -4 4 2 2 2 2

2 2 2 2c c 4a b | a b |1

2ab4a b 4a b- -= - = =

(using c2 = a2 + b2)

89. (b) Let dx)x1(sinxsin

xsin1

011

1

-+= ---

I ...(1)

[since )]x1(sin)xx2(cos 121 -=- --

---

+--=

1

011

1dx

xsin)x1(sin)x1(sin

I . . ..(2)

Adding (1) and (2)

1

0

12I 1 dx 1 I2

= = =

90. (c) rnr50

0xr

50 )x2()3x2(C -

=--

50 0 n 50 1 n 10 1C (2x 3) (2 x) C (2x 3) (2 x)

-= - - + - -50 2 n 2 50 n

2 50C (2x 3) (2 x) ...... C (2x 3)-+ - - + -

21

.....xCxC)1x( 4915050

05050 +-=-=

Coeff. of x25 = 2550 C- .

91. (a) Since iz z 1 iArg Argz iz 1 i

+ + = - - 2(i 1)Arg Arg i ACB

2 2 2+ p p= = = = .

So orthocentre is 0 + 0i.

92. (d) 211 CCC +a

2

a b b a bb c c b c

a 2b c b c 0

a + a +a + a +

a + a + a +

a b b a bb c c b c 0

0 b c 0

a + a += a + a + =

a +93. (b) 322311 CcosCCandCsinCC q+q-

0cossincos10sin01

)(fq-q

qq-

=q

Again 213 RcosRsinR q+q- we get

= 1100

cos10sin01

=qq-

16

f =

p .

94. (a) The common root must satisfy

0)rpxx7x()qpxx5x( 2323 =+++-+++

i.e., 0rqx2 2 =-+-Sum of common roots = 0 7x,5x 21 -=-= .

95. (a) If x = 33 37 49 x+ 3 3 3 37 49 3 7 49( 7 49)= + + +

3 3x 56 21x x 21x 56 0 = + - - = Product of roots = 56.

96. (d) Number of groups having 4 boys, 1 girl

= 3C.C 13

44 =

Number of groups having 3 boys, 2 girls

= 12C.C 23

34 =

Number of groups having 2 boys, 3 girls

= 4 32 3C . C 6=So, total number of dolls= 3 1 + 12 2 + 6 3 = 45.

97. (c) Let the roots be

40rr1r1

r1aar,ar,a,

ra,

ra 2

22

2=

++++ .

Also 221 1 1 1 r ra rr

+ + + + 210 a 4 a 2= = =

Now product of roots = s a5 = s

32|a||s| 5 ==98. (b) Total cost

= 2300 x 30010 2 200

x 600 x

+ + ;

266000 5xx+=

Which is minimum if x = 60.99. (d)

2 2n

r 1

n(n 1) n(n 1)(2n 1) n (n 1)(r) 3 2 8

1 (2n 1) n(n 1)=

+ + + +D = -

+ +

R1 n (n + 1)R3 = 0; So sum = zero.100. (c) We must have

]1sec,1[x1xsec0 1 - .Hence option (c) is the right choice.

101. (d) (cos 1)(cos 2) 0q - q - =

cos 1 or 2 q = 2cos =qNot possible. cos 1 0 or 2q = q = p &hence 2 solution.

102. (c) 1 1sin x 3sin a2 2 2 2

- -p p p p- -

1sin a6 6

-p p -

6sina

6sin p

p-

; 21a

21 - .

22

103. (a) y = x + sin x ; 02xcos2xcos1

dxdy 2 =+=

y is an increasing function. Hence nomaximum point.

104. (a)3 3

6 6

dx dxsin 2x 2sin x cos x

p p

p p=

3 23

66

1 sec xdx 1 (log x tan x)2 tan x 2

pp

pp

= =

e1 1 1 1log 3 log .2 log 3 log 32 2 23

= - = = 105. (c) (1 + x)m (1 x)n

= 2m(m 1)1 mx x ......

2- + + +

2n(n 1)1 nx x ......2- - + +

coeff. of x = m n = 3 ...(1)coeff. of

x2 = 2

)1n(n2

)1m(m -+- mn = 6 ...(2)

Solving (1) and (2)we get m = 12, n = 9

106. (c) | x 3 | is always positive. Therefore f(x) 5. Therefore greatest value = 5.

107. (a) Distance between centres < sum of radiibut > difference of radii. 5 < r + 3 and 5 >r 3, 2 < r and 8 > r. \ 2 < r < 8.

108. (d) f(x) = 3 3

3 330 x 30 xlog f ( x) log30 x 30 x

- + - = + - 3

330 xlog f (x)30 x

-= - = - + )x(f is an odd function.

Hence, -

=3

3

0dx)x(f .

109. (d) Using b b

a af (x)dx f (a b x) dx= + -

( )n

1a n

I (a x)f (a x)x dx-

= - -n

1a n

a f (x(a x)) dx-

= - - I

1

1 22

I a2I aII 2

\ = =

110. (a) Clearly (0, 0) is a common point on these 2curves. Slope of tangents at (0, 0) is 1, socommon tangent is y 0 = 1(x 0) y = x.

111. (d) 2x16 - is defined in [4, 4].

]xcos1[sin 1 +- is defined if1 1 cos x 2 cos x 1 + <

x [ 4,0) (0,4] - 112. (c) Centre C1 (2, 3), C2 (1, 1), r1 = 4, r2 =

1. We have C1C2 = 5 = r1 + r2. Hence 3common tangents can be drawn.

113. (b) The lines x 2y = 0 and x 2y + k = 0 areparallel. The distance between 2 lines

= 53k3)2(1

k2

==-+

114. (c) The probability that both of them did not

occur = 1 2P(A) P(B) (1 p )(1 p )= = - -Therefore Probability that atleast one

happens = 1 )B(P)A(P = 1 (1 p1)(1 p2) = p1 + p2 p1p2.

115. (c) Probability of success = 21

63 =

21q,

21p == ; For exactly 4 successes

required probability

= 12835

21

21C

34

47 =

23

116. (c) Now there are only two possibilities :-Either head appears odd no. of times = eventA Or head appears even no. of times = eventB Since both are mutually exclusive and

equally likely. Therefore P(A) = P(B) = 21

.

Therefore required probability = 21

.

117. (c) )given(y1

1xx)x(f =-

=

x111x

1x

1xx

1x

)y(f,x

1xy -=--=

--

-=-=\

118. (b) Let us solve y2 = x and y = x2, x4 x = 0

0)1x(x 3 =-1x,0x ==\

1y,1xand0y0x ====\Therefore, points are (0, 0), (1, 1)

\ Area required

= 31

3xx

32dx)xx(

1

0

32/3

1

0

2 =

-=-

119. (a) x2xsindxdy +=

y = cxcosx2x2xcos 2

2+-=+ .

120. (b) 1iziz1)given(1|w|

iziz1 =

--==

--

1 1

2 2

z | z | |1 iz | | z i |z | z |

= - = -Q

| 1 i(x iy) | | (x iy) i | - + = + -| (1 y) ix | | x i(y 1) | + - = + -

2 2 2 2[(1 y) ( x) ] [x (y 1) ] + + - = + -2 2 2 2(1 y) x x (y 1) + + = + -

1y2yxxyy21 2222 +-+=+++or, 4y = 0 \ y = 0From this it is known that the locus of z, isy = 0, which is a real axis. Therefore, z issituated on real axis.

121. (b) Equation of a plane through the point(0, 4, 3) isa (x 0) + b (y 4) + c (z 3) = 0 ... (1)It passes through ( 2, 2, 1) and ( 1, 1, 1)if a + 3b + c = 0 and a 3b 4c = 0

6c

5b

9a

-==

-

\ From (1), equation of plane is 9 (x 0) +5 (y 4) 6 (z 3) = 0 or 9 x 5y + 6z + 2 = 0.It is satisfied by ( 1, 5, 3).

122. (a)

- 2, function isagain linear, hence continuous.Thus, function is continuous for all realvalues of x.

123. (d) When a line lies in a plane, then it is at rightangles to the normal to the plane. Here, d.r.of the line are a, b, c, and d.r. of the planeare being taken as A, B, C So, we must haveaA + bB + cC = 0.

124. (a) In the first situation, (2m + 1)2 (P2 + Q2)= P2 + Q2 + 2PQ cos a ......(1)In the second situation, (2m - 1)2 (P2 + Q2)= P2 + Q2 + 2PQ cos(900 a ) .....(2)From (1), (P2 + Q2) (4m2 + 4m)= 2PQ cos a and from (2)(P2 + Q2) (4m2 - 4m) = 2PQ sin a

Dividing we get tan a = 1m1m

+-

125. (d) We have .x,7x4)x(f 3 R-= f is one-one. Let x1, x2R and f (x1) = f(x2).

32

31

32

31 x4x47x47x4 =-=-

.0xxxx 323

13

23

1 =-=

.0)xxxx()xx( 22212

121 =++-

24

.04

x32

xx)xx(2

22

2121 =

+

+-

x1 x2 = 0, because the other factor isnon-zero. x1 = x2 \ f is one-one.f is onto. Let k R any real number.

3/13

47kxk7x4k)x(f

+==-=

andkbecause,4

7kNow3/1

RR

+

33/13/1

47k4

47kf

+=

+

7

k74

7k4 =-

+=

\ k is the image of 3/1

47k

+

\ f is onto. \ f is a bijective function.

ENGLISH PROFICIENCY126. (b) Transgressor is a person who breaks the

law i.e. a law breaker.127. (c) Predilection means preference toward

something whereas aversion meansopposition.

128. (d)129. (d) Forecast is used to predict or estimate a

future event.130. (b) Avenged means to inflict harm in return for

an injury or wrong done to oneself oranother.

131. (a)132. (b) Ambidextrous means both hands. The

ambidextrous person can perform an actionwith either hand having equal dexterity inthe action.Writing is themost striking ofthese actions.

133. (c)134. (d)135. (c)136. (d)

137. (b)138. (a) The author states how Gandhi showed the

mirror to the masses on how the cruelsystem is deteriorating the country andurged them to stand up for themselves.

139. (b) The rise of Gandhi empowered the peoplewhich thus made the country strong.

140. (c) Gandhi fought the unjust system that wasexploiting the peasants and workers.

LOGICAL REASONING

141. (b)M O Q S A C E G+2 +2 +2 +2 +2 +2

P R T V+2 +2 +2

O Q S U+2 +2 +2

142. (a) Swimming is done in the river.Hiking is done from mountain.

143. (b) In the remaining, vowel is present.144. (d)

2 8 18 32 50 72

+6 +10 +14 +18 +22

+ 4 + 4 + 4 + 4145. (c) Moving clockwise, the terms are :

5 2 + 2 = 1212 2 + 2 = 2626 2 + 2 = 5454 2 + 2 = 110

So, missing number = 110 2 + 2 = 222146. (a)

147. (a)D

AC

148. (d)149. (d) All the figures provided in the options are

present in the 'collection' except for D whichat first sight might seem similar to the figurein the first column-second row object, butclose examination would reveal that it has 5teeth instead of 4 teeth present in the abovementioned figure belonging to thecollection.

150. (d)